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We describe a new method for solving Maxwell’s equations that couples scalar surface integral equations (SIEs) with an iterative implementation of the (vector) boundary conditions. The formulation can handle multiple homogeneous regions and, in computational efficiency, compares favorably with the more conventional volume integral method. The system equations are solved iteratively in three stages: (1) iterations to solve the coupled scalar SIE; (2) iterations to implement vector boundary conditions; and (3) iterations to calculate surface fields in three dimensions. Numerical results for a sphere excited by a plane wave and for an oblate spheroid in a half-space excited by a rectangular surface loop show that the method is stable for a wide range of conductivity contrasts and gives reasonable results for the electromagnetic response from the resistive up to the inductive limit.

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